What are sin and cos and why are they used so frequently in math?
In: 6
In short: sin and cos are function. You give them a number and they spit out a number.
The number they spit out follows an pattern that’s a wave. The output bounces between -1 and 1.
Why are they used so much? Because the rate that they bop between -1 and 1 maps to how far up or down (for sin), or side to side (for cos) is for a particular angle. This is useful for right angled triangles because because we can take the long edge of a right angle triangle, an angle the edge is pointing and then we can tell how much of that is up and down, and how much is side to side (the other edges of the triangles). This is useful even when we don’t have a physical triangle, like you can take the speed of a rock thrown, the angle it was thrown at and then know how fast it’s moving up and down or left and right, so we could tell where it would hit the ground for example. Any vector ( a thing with a magnitude and direction) can be broken down to get how much of it is moving up and down or side to side .
Additionally theyre used to represent things which go up and down. Like waves. We can change their frequency and amplitude so if we just find the numbers we can then use sin waves to represent anything that goes back and forth regularly, like a swing. We could then use that to predict where that swing would be at any given time.
So they’re useful for triangles imaginary triangles and things which go backwards and forwards a lot. That’s a lot of things. So they pop up a lot.
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